Relatively straight forward. All missions in the game give credit towards this achievement. You can get missions from most stations, the mercenaries and merchant's guilds also provide missions for you to complete. They range from hauling cargo, hunting targets, defending ships and rescuing merchants. Main story missions also give credit towards this. You can only take 4 station missions at any one time. Story missions do not take up your private mission spaces.
Missions range in difficulty based on how kitted your ship is. You can tell how difficult a quest will be for your individual ship's rating by the color of it's text while selecting missions; blue for negligible, green for low, white for normal, orange for hard and red for extreme.